标题： 非线性模型预测控制在安全移动机器人导航中的逐步指南 显示英文标题

标题： A Step-by-step Guide on Nonlinear Model Predictive Control for Safe Mobile Robot Navigation

摘要： 设计一种模型预测控制（MPC）方案，使移动机器人能够在充满障碍物的环境中安全导航，是机器人学中一个复杂但重要的任务。 在本技术报告中，安全性是指在存在扰动和测量噪声的情况下，确保机器人遵守状态和输入约束并避免与障碍物发生碰撞。 本报告提供了一个逐步实现非线性模型预测控制（NMPC）方案的方法，以解决这些安全要求。 许多书籍和综述论文对线性模型预测控制（LMPC）\cite{bemporad2007robust,kouvaritakis2016model}，NMPC\cite{rawlings2017model,allgower2004nonlinear,mayne2014model,grune2017nonlinear,saltik2018outlook}以及它们在各种领域（包括机器人学）中的应用提供了全面的概述\cite{nascimento2018nonholonomic,nguyen2021model,shi2021advanced,wei2022mpc}。 本报告的目的不是重复这些详尽的综述。 相反，它特别关注NMPC作为安全移动机器人导航的基础。 目标是从理论概念到数学证明和实现提供一条实用且易于理解的路径，强调安全性和性能保证。 本报告旨在为研究人员、机器人工程师和实践者提供帮助，以弥合理论NMPC公式与实际机器人应用之间的差距。 本报告不一定需要长期固定不变。 如果有人发现所呈现理论中的错误，请通过提供的电子邮件地址与我们联系。 如需，我们将很高兴更新文档。 显示英文摘要

摘要： Designing a Model Predictive Control (MPC) scheme that enables a mobile robot to safely navigate through an obstacle-filled environment is a complicated yet essential task in robotics. In this technical report, safety refers to ensuring that the robot respects state and input constraints while avoiding collisions with obstacles despite the presence of disturbances and measurement noise. This report offers a step-by-step approach to implementing Nonlinear Model Predictive Control (NMPC) schemes addressing these safety requirements. Numerous books and survey papers provide comprehensive overviews of linear MPC (LMPC) \cite{bemporad2007robust,kouvaritakis2016model}, NMPC \cite{rawlings2017model,allgower2004nonlinear,mayne2014model,grune2017nonlinear,saltik2018outlook}, and their applications in various domains, including robotics \cite{nascimento2018nonholonomic,nguyen2021model,shi2021advanced,wei2022mpc}. This report does not aim to replicate those exhaustive reviews. Instead, it focuses specifically on NMPC as a foundation for safe mobile robot navigation. The goal is to provide a practical and accessible path from theoretical concepts to mathematical proofs and implementation, emphasizing safety and performance guarantees. It is intended for researchers, robotics engineers, and practitioners seeking to bridge the gap between theoretical NMPC formulations and real-world robotic applications. This report is not necessarily meant to remain fixed over time. If someone finds an error in the presented theory, please reach out via the given email addresses. We are happy to update the document if necessary.